Categorical semantics for arrows

Journal of Functional Programming (Impact Factor: 0.52). 07/2009; 19(3-4):403-438. DOI: 10.1017/S0956796809007308
Source: DBLP


Arrows are an extension of the well-established notion of a monad in functional programming languages. This article presents several examples and constructions, and develops
denotational semantics of arrows as monoids in categories of bifunctors C^op x C -> C. Observing similarities to monads -- which are monoids in categories of endofunctors C -> C
-- it then considers Eilenberg-Moore and Kleisli constructions for arrows. The latter yields
Freyd categories, mathematically formulating the folklore claim “arrows are Freyd categories”.

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